Symmetries of highly excited atomic hydrogen: Quadratic Zeeman splitting distorted by fine-structure effects

Abstract

In this paper we consider the same system. But the magnetic field is assumed to be weaker so that the diamagnetic splitting is comparable with the fine structure of the unperturbed atom. Relativistic effects conserve the abovementioned symmetry and it seems unlikely that they will lead to essentially new effects. Nevertheless, we will show that the hydrogen atom in magnetic field possesses yet another symmetry. The latter does not lead to any interesting phenomena in the nonrelativistic situation. However, when the relativistic effects are present it gives birth to another type of doublet. Here we analyze the dynamical symmetry origin of these doublets and other peculiar relativistic distortions of the quadratic Zeeman spectra in the atomic hydrogen. We give a physical explanation of the earlier results of @19# where the discrete WentzelKramers-Brillouin-Jeffreys ~WKBJ! method was used to solve the quantum perturbation theory equations of the problem.